I want to implement a racial feature that gives the following benefit: "When you finish a long rest, you gain proficiency with a tool or weapon that you don't already have. This proficiency lasts until the end of your next long rest." Is there a way to do this?

Yes. Attach the following Modifier to the racial trait and it should generate a dropdown in the character builder: 

• Modifier: Proficiency->Subtype: Choose a Weapon/Tool from the PHB

The player need only back into the character builder to select a new tool or weapon each time they take a long rest.

PS- I hope that helps. 

Thanks, somehow it didn't occur to me that the player could simply go back into the character builder.